WITHOUT USING TRIGONOMETRIC TABLE,PROVE-

sin 5 tan 22 sec 60 tan 68 sec 85 = 2

Dear Student!

Here is the answer to your question.
 
sin5⁰ tan22⁰ sec60⁰ tan 68⁰ sec85⁰
 
= sin5⁰ tan22⁰ sec60⁰ tan (90⁰ - 22⁰) sec (90⁰ - 5⁰)
 
= sin5⁰ tan22⁰ × 2 × cot 22⁰ cosec5⁰  [ tan(90 - θ)= cot θ, sec(90 - θ)= cosec θ]

= 1 × 1 × 2
 
= 2
 
Cheers!

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LHS = sin 5  tan 22  sec 60  tan ( 90 - 22)  sec (90 - 5)

= sin 5  tan 22  sec 60  cot 22  cosec 5

= sin 5  tan 22  sec 60  1/ tan 22  1/ sin 5

= sec 60 = 2 = RHS

TIP : Always 1st find the pair of angles whose sum is equal to 900.

for eg, 5 + 85 and 22 + 68 in this Q.

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